Various means have been considered to prevent a baby from throwing off its covers and becoming chilled. Attempts to keep a child covered have included blankets which are secured to a bed. With this type of blanket, the blanket is secured to a bed, and the child is then secured under the blanket, for example, by shoulder straps. Blankets which secure a child to a bed are taught by U.S. Pat. Nos. 2,503,427 and 2,702,385. Parents may find these blankets too confining for their children. Moreover, a child may become tangled in the straps and confining blanket, which may frighten the child or lead to injury. More recent efforts have included blankets which are secured about the child, but which are not attached to a bed. Of these patents, U.S. Pat. No. 5,243 to Barnes, U.S. Pat. No. 2,968,044 to Dudley, and U.S. Pat. No. 4,295,230 Blogett are of note. Barnes teaches a rectangular blanket in which the lower portion of the rectangle is formed into a pocket for receiving a child. The child is placed into the pocket and then the sides of the blanket are then rolled around the child. Straps are used to secure the blanket about the child's waist. Although blankets of this design provide a child with more freedom of movement than those blanket which attach to a bed, the Barnes blanket uses a lot of material which must be folded about the baby and left to flop about the baby's head. All this material restricts the baby's movement, adds weight to the blanket, and increases the cost of production. Blankets of a simpler, more efficient design are taught by Dudley and Blogett. Both Dudley and Blogett teach blankets of a bag design which are secured to a child. In the Blogett patent, the bag-like blanket is secured to the child by releasably fastened shoulder straps. Although the child can be easily inserted into the bag-like portion of the blanket, some manipulation of the child and the blanket is necessary to fasten the shoulder straps. All the activity necessary to secure a child within the blanket may be difficult with a squirming child and may also result in the unfortunate consequence of waking a sleeping child. Dudley teaches a bag-like blanket which is secured about a baby's waist using a draw-string tie. The Dudley blanket presents the problem of a baby becoming tangled in the tie string or choking on the string.